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June 30, 2015

C 2015 American Chemical Society

Complex Evolution of Built-inPotential in Compositionally-GradedPbZr1�xTixO3 Thin FilmsJoshua C. Agar,†,‡ Anoop R. Damodaran,† Gabriel A. Velarde,‡ Shishir Pandya,† R. V. K. Mangalam,† and

Lane W. Martin*,†,‡,§

†Department of Materials Science and Engineering, University of California, Berkeley, Berkeley, California 94720, United States, ‡Department of Materials Scienceand Engineering, University of Illinois, Urbana�Champaign, Urbana, Illinois 61801, United States, and §Materials Science Division, Lawrence Berkeley NationalLaboratory, Berkeley, California 94720, United States

Susceptibility to electric field, stress, andtemperature make ferroelectrics idealcandidates for a wide variety of nano-

scale applications ranging from memories,1

to actuators, to infrared sensors, to pyro-electric electron emitters.2�4 The responseof a ferroelectric is strongly coupled to bothits atomic-scale crystal and nanoscale domainstructures wherein small perturbations toeither can dramatically influence the proper-ties. The implementation of modern thin-filmdeposition techniques and increased avail-ability of lattice-matched substrates has en-abled the use of epitaxial strain tomanipulatethe crystal and domain structure of thesematerials and provides a means to tunesusceptibilities.5 In recent years, there hasbeen recognition that epitaxial strain need

not be homogeneous in nature, and re-searchers have looked to leverage the abilityto deterministically create inhomogeneousstrains to further control materials.6�11 Thepresence of strain gradients are particularlyinteresting in ferroelectrics because of thepotential for strong so-called flexoelectriceffects. Flexoelectricity refers to the linearcoupling of a strain gradient (∂εij/∂xk) andthe polarization (Pi) of a material, mediated bythe fourth-rank flexoelectric tensor (μijkl). Bol-stered by the ability to produce large straingradients, on theorder of 105m�1, in thinfilmsthrough the use of mechanical stress,12�14

defect and domain engineering,8,9,15,16 andcompositional gradients,6,7 there has beena reemergence of interest in flexoelectricity.Such large strain gradients produce large

* Address correspondence tolwmartin@berkeley.edu.

Received for review April 16, 2015and accepted June 30, 2015.

Published online10.1021/acsnano.5b02289

ABSTRACT Epitaxial strain has been widely used to tune crystal and domain

structures in ferroelectric thin films. New avenues of strain engineering based on

varying the composition at the nanometer scale have been shown to generate

symmetry breaking and large strain gradients culminating in large built-in

potentials. In this work, we develop routes to deterministically control these built-

in potentials by exploiting the interplay between strain gradients, strain

accommodation, and domain formation in compositionally graded PbZr1�xTixO3heterostructures. We demonstrate that variations in the nature of the composi-

tional gradient and heterostructure thickness can be used to control both the crystal and domain structures and give rise to nonintuitive evolution of the

built-in potential, which does not scale directly with the magnitude of the strain gradient as would be expected. Instead, large built-in potentials are

observed in compositionally-graded heterostructures that contain (1) compositional gradients that traverse chemistries associated with structural phase

boundaries (such as the morphotropic phase boundary) and (2) ferroelastic domain structures. In turn, the built-in potential is observed to be dependent on

a combination of flexoelectric effects (i.e., polarization�strain gradient coupling), chemical-gradient effects (i.e., polarization�chemical potential

gradient coupling), and local inhomogeneities (in structure or chemistry) that enhance strain (and/or chemical potential) gradients such as areas with

nonlinear lattice parameter variation with chemistry or near ferroelastic domain boundaries. Regardless of origin, large built-in potentials act to suppress

the dielectric permittivity, while having minimal impact on the magnitude of the polarization, which is important for the optimization of these materials

for a range of nanoapplications from vibrational energy harvesting to thermal energy conversion and beyond.

KEYWORDS: ferroelectrics . PbZr1�xTixO3. thin films . compositionally-graded heterostructures . permittivity

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flexoelectric effects (or effects that mimic thosearising from flexoelectricity) that can alter the ferroicresponse of materials,17,18 allow for mechanically in-duced ferroelectric switching,12�14 drive horizontalshifts of ferroelectric hysteresis loops,7,19�21 and allowfor independent tuning of typically coupled ferroelec-tric susceptibilities.6,7,10

Despite this renewed interest, there is widespreaddissensus regarding how to define, quantify, measure,and/or decouple flexoelectric effects fromother coupledelectromechanical responses. In this context, there arediscrepancies as to the magnitude and even the sign offlexoelectric coefficients in materials,18 wherein experi-mentally measured values22�25 are typically ordersof magnitude larger than those predicted from firstprinciples.26�28 There is growing concern that additionalcontributions that can mimic flexoelectric response(which are unable to be decoupled in macroscalemeasurement, but are excluded from first-principles cal-culations) could possibly account for these discrepancies.These ancillary contributions include: strain-gradient-driven inhomogeneous segregation of space charges,15,29

chemical gradients,20,21,30 localized potential gradients atnanodomain boundaries,31,32 polarization gradients (inthe presence of screening charges which minimizedepolarization),33 surface piezoelectricity,17,34,35 etc.Only recently has there been a concerted effort tounderstand the relative importance of the intrinsicflexoelectric and such ancillary contributions to themacroscopic response of materials. While the relativeimportance of these contributions is scientifically sig-nificant, what is most important from an engineeringperspective is to understand how to maximize thecollective influence of all these effects on the propertyof interest, in this case the built-in potential.Here, we explore deterministic routes to control the

macroscale built-in potential (i.e., the horizontal shiftof the ferroelectric hysteresis loop) by exploiting thenanoscale interplay between chemistry, strain gradients,strain accommodation, and domain formation incompositionally-graded PbZr1�xTixO3 (PZT) heterostruc-tures. We find that variations in the nature of the compo-sitional gradient and heterostructure thickness can beused to control both the crystal and domain structuresgiving rise to a nonintuitive evolution of the built-inpotential which does not scale directly with themagnitude of the strain gradient as would be expected.Large built-in potentials are instead observed incompositionally-graded heterostructures that contain(1) compositional gradients that traverse chemistriesassociated with structural phase boundaries (such asthe morphotropic phase boundary) and (2) ferroelasticdomain structures. In turn, the built-in potential is ob-served to be dependent on a combination of flexoelectriceffects (i.e., polarization�strain gradient coupling),chemical-gradient effects (i.e., polarization�chemicalpotential gradient coupling), local inhomogeneities

(in structure or chemistry) that enhance strain (and/orchemical potential) gradients suchas areaswithnonlinearlattice parameter variation with chemistry or near ferro-elastic domain boundaries. Regardless of origin, largebuilt-in potentials act to suppress the dielectric permittiv-ity, while havingminimal impact on themagnitude of thepolarization. Such observations are important to providenew routes to decouple ferroic susceptibilities and forthe optimization of figures of merit for a range of nano-scale applications including piezoelectric-based vibra-tional energy harvesting36�38 and pyroelectric-basedthermal energy conversion.6,39,40

RESULTS AND DISCUSSION

Inspection of the composition�temperature phasediagram for the PbZr1�xTixO3 system (Figure 1a)

Figure 1. (a) PbZr1�xTixO3 phase diagram, adapted from B.Jaffe et al.41 (b) Bulk lattice parameter (shown in black) andcalculated misfit strain (shown in blue) spanning across thePbZr1�xTixO3 phase diagram. (c) Schematic illustrations ofPbZr0.8Ti0.2O3 T PbZr0.2Ti0.8O3/SrRuO3/GdScO3 (110) het-erostructures: 50, 75, 100, and 150 nm thick. (d) Schematicillustrations of 100 nm thick PbZryTi1�yO3 T PbZrxTi1�xO3/SrRuO3/GdScO3 heterostructures spaning various composi-tional ranges (sample name: (x,y)).

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reveals a structural competition between tetragonaland rhombohedral symmetry on the Ti- and Zr-richsides, respectively. Likewise, the room-temperaturelattice parameter-composition evolution (Figure 1b)reveals that the lattice parameters do not vary linearlywith composition and instead change rapidly near themorphotropic phase boundary (MPB, x = 0.48).On the basis of this information, we focused on

compositionally-gradedheterostructures PbZr1�yTiyO3S

PbZr1�xTixO3/30 nm SrRuO3/GdScO3 (110) (a = 5.45 Å,b = 5.75 Å, c = 7.93 Å, pseudocubic apc = 3.96 Å) grownusing pulsed-laser deposition following previously estab-lished procedures (see details in the Methods section).6,7

Growth on GdScO3 substrates provides lattice mis-matches between �4.6 to 2% as one transitions fromPbZrO3 to PbTiO3 (Figure 1b, right axis). In all cases, thecomposition of the bottom-most PbZr1�xTixO3 layer ischosen to be the composition with the least latticemismatch to the substrate and all compositional gradi-ents are controlled to be linear in nature. All hetero-structures are named on the basis of the variation of theZr-content upon transitioning from the substrate inter-face (x) to the free surface of the film (y) in the form (x,y).In this work, we studied six compositionally-graded-

heterostructure variants, which are separated into twogroups for discussion. This first is a series probing theeffects of film thickness variation wherein we probe 50,75, 100, and 150 nm thick (20,80) compositionally-graded heterostructures (Figure 1c). These thicknesseswere selected because they permit a large variation inthe magnitude of the maximum theoretical averagestrain gradient (from8.7� 105m�1 to 2.9� 105m�1 forthe 50 and 150 nm thick heterostructures, respectively).Note that the theoretical strain gradients can be ob-tained by taking the difference in the misfit strainbetween the substrate and the bulk lattice parameterof the parent phases at the substrate�film interface andthe free surface and dividing by the film thickness;values for lattice parameters are provided (Figure 1b).In addition, these variations in thickness also provide apathway to alter the form and density of the ferroelasticdomain structure.42

The second series of heterostructures probes theeffects of varying the nature of the compositionalgradient and focuses on 100 nm thick (20,45), (40,60),and (20,80) heterostructures (Figure 1d). This series ofcompositional gradients was selected for two reasons:(1) the (20,80) heterostructure (4.3 � 105 m�1) hasapproximately double the strain gradient of the(20,45) (i.e., 2.2 � 105 m�1) and (40,60) (i.e., 2.5 �105 m�1) heterostructures which allows us to probethe effect of varying strain gradient magnitude and(2) the (20,80) and (40,60) heterostructures includethe MPB composition while the (20,45) heterostruc-ture does not, allowing the role of the nonlinear latticeparameter evolution near theMPB in this system to beprobed.

X-ray diffraction θ-2θ and reciprocal space mapping(RSM) studies found all heterostructure variants to besingle-phase, fully epitaxial, and (001)-oriented regard-less of thickness or gradient design (wide-angle, θ-2θX-ray diffraction patterns are provided, SupportingInformation, Figure S1). RSM studies were completedabout the 103- and 332-diffraction conditions ofthe films and substrate, respectively (Figure 2). Thepositions of the bulk and strained peaks for theparent phases are provided for reference. Focusingon the thickness series of (20,80) heterostructures(Figure 2a�d), as expected the Qy-values span con-tinuously between the theoretical strained peak posi-tions of the parent phases. As the thickness of theheterostructures increases, however, there is a slightincrease in spectral weight toward lower Qx-values anda slight decrease in spectral weight near the expectedlattice parameter for strained PbZr0.8Ti0.2O3. A quanti-tative measure of this relaxation can be obtained bycomparing the logarithmically-scaled, weighted-meanintensity of the 103-diffraction condition to the theo-retical strained and relaxed average peak positions(a description of the methodology used is provided,Supporting Information, Figure S2). From these ana-lyses, both the 50 and 75 nm thick (20,80) heterostruc-tures (Figure 2a,b) are found to be coherently strainedto the substrate (within experimental resolutionlimits). As the thickness of the (20,80) heterostructureis increased to 100 nm (Figure 2c) and 150 nm(Figure 2d), the relaxation from the theoretical strainedpeak position increases to ∼10.6% and ∼22.3%, re-spectively. All told, these observations imply that strainrelaxation increases with film thickness as would typi-cally be expected.43

Similar analyses on the 100 nm thick compositionally-graded heterostructures with different gradient forms[i.e., (20,45) (Figure 2e), (40,60) (Figure 2f), and (20,80)(Figure 2c)] again reveal that the Qy-values spancontinuously between the theoretical strained-peakpositions of the parent phases. Following the sameprocedure noted above, the (20,45) heterostructuresare found to be coherently strained to the substrate(within the experimental resolution limits), but the(40,60) heterostructures exhibit partial strain relaxation(∼26.7% relaxed from the theoretical strained peakposition). The minimal (or negligible) strain relaxationin the (20,45) heterostructures can be readily under-stood since the films possess uniform bulk tetragonalstructure and smaller lattice parameter variation acrossthe thickness of the heterostructure. On the otherhand, the (40,60) heterostructures possess more thandouble the amount of strain relaxation than the (20,80)heterostructures despite having approximately half thetheoretical strain gradient. This discrepancy can be un-derstood by considering the lattice mismatch betweenthe substrate and the bottom-layer PbZr1�xTixO3, whichin the (20,80) heterostructures is only 0.15% tensile as

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compared to �1.2% compressive in the (40,60) hetero-structures. Thus, the larger lattice mismatch at the sub-strate�film interface likely begetsmore pronounced andrapid strain relaxation.The key insight from these analyses is that, regard-

less of the film thickness and the nature of the compo-sitional gradient, the heterostructures retain a largemajority (if not all) of the epitaxial strain imparted bythe substrate. This stands in contrast towhat is typicallyobserved in homogeneous films of the various parentmaterials (100 nm thick PbZr0.2Ti0.8O3, PbZr0.52Ti0.48O3,and PbZr0.8Ti0.2O3 heterostructures grown on GdScO3

substrates reveal 0, 84.0, and 45.3% strain relaxation,respectively, Supporting Information, Figure S3). Thus,consistent with what has been observed in group IVand III�V semiconductor systems,44,45 these resultsdemonstrate that the presence of the compo-sitional gradient (and in particular, those with minimallattice mismatch at the film�substrate interface) pro-vides a pathway to retain large residual strains and

strain gradients not possible in homogeneousheterostructures.Not only does changing the nature of the composi-

tional gradient and heterostructure thickness impactthe structure and strain state of the heterostructures,but it also can give rise to and vary both the density andnature of ferroelastic domains.43,46 To image thesenanoscale ferroelastic domains we conducted out-of-plane piezoresponse force microscopy (PFM) studies.Again, focusing first on the thickness series of (20,80)heterostructures, the 50 nm thick heterostructuresare observed to exhibit a monodomain structure(Figure 3a), consistent with expectations for a (00l)-oriented, highly compressively strained tetragonal ferro-electric (such as Ti-rich PbZr1�xTixO3). Upon increasingthe thickness of the heterostructures to 75 and 100 nm,c/a/c/a domain structures (consisting of out-of-planepolarized c domains and in-plane polarized a domains)with density and domain width increasing with hetero-structure thickness are observed (Figure 3b; data shown

Figure 2. Reciprocal space mapping about the 103-diffraction conditions for PbZryTi1�yO3 T PbZrxTi1�xO3/SrRuO3/GdScO3

(110) heterostructures (sample name: (x,y)) (a) 50 nm (20,80), (b) 75 nm (20,80), (c) 100 nm (20,80), (d) 150 nm (20,80),(e) 100 nm (20,45), and (f) 100 nm (40,60). Dashed lines represent the coherently strain (vertical) and cubic (angled) latticeparameters and the expectedpeakpositions for bulk (black) and strained (orange) versions of theparent phases are labeled ineach graph. The percentage of strain relaxation is also noted.

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only for the 100 nm heterostructure for brevity).Again, such a domain structure is typically observedonly in tetragonal ferroelectrics (Supporting Informa-tion, Figure S4a).43,47 Finally, for the 150 nm thickheterostructures, a complex mosaic-like domain struc-ture is observed (Figure 3c), indicating that, at least atthe surface, the tetragonal-like domain structure is nolonger stabilized and instead the domain structure isconsistent with typical rhombohedral PbZr1�xTixO3 het-erostructures (Supporting Information, Figure S4b).These observations can be understood by consideringthe driving forces for ferroelastic domain formation andthe observed crystal structures. In the thinnest films,coherency is maintained and the large compressivestrain drives the manifestation of a tetragonal-likecrystal and monodomain structure. At intermediatethicknesses, the growing strain energy results in slightstrain accommodation, but the residual epitaxial strainis enough still to stabilize the tetragonal crystal anddomain structure. Finally, in the thickest heterostruc-tures, more significant relaxation (especially at the freesurface) results in loss of coherency to the substrate andrelaxation (at least at the surface) to the parent rhom-bohedral phase (and domain structure).We have also probed the effect of changing the

nature of the compositional gradient on the domainstructure evolution. PFM studies of both the 100 nmthick (20,45) (Figure 3d) and (40,60) (Figure 3f) hetero-structures reveal a monodomain structure; onceagain, similar to, those observed in highly compressivelystrained tetragonal ferroelectrics. Such a monodomainstructure in the (20,45) heterostructures is unsurpris-ing, since the film is entirely on the tetragonal sideof the phase diagram where compressive strains actto stabilize the c phase. Conversely, the presence ofa monodomain structure in the (40,60) heterostruc-tures is unexpected as these heterostructures havemany attributes which should drive the formation ofa polydomain structure. First, the (40,60) heterostruc-tures have a considerably larger average misfit strainand subsequent relaxation (as compared to the (20,45)heterostructures). Second, they possess a large frac-tion of the heterostructure compositionally near theMPB where the flattened energy landscape betweenthe structural variants facilitates ferroelastic domainformation48 and nanodomain structures.49,50 Third, the

top ∼50% of the film is compositionally such that itshould have rhombohedral structure. Likely, the presenceof the continually increasing compressive strain state,which transitions from �1.2% compressive at the film�substrate interface to �3.2% compressive at the freesurface, enables the retention of considerablymore strainthan is achievable in homogeneousfilms, thereby stabiliz-ing the tetragonal-like crystal and domain structure.This understanding of how the nature of the com-

positional gradient and the heterostructure thicknesscan be manipulated to engineer the strain gradientand domain structure is important to obtain a com-prehensive picture of how built-in potential and prop-erties evolve in these heterostructures. To quantify thebuilt-in potential, ferroelectric hysteresis loops weremeasured for the various heterostructures (for brevity,we show characteristic hysteresis loops measured at1 kHz, Figure 4a,b, but loops at other frequencies arealso provided, Supporting Information, Figure S5a�f).Similar to homogeneous ferroelectric thin films, allheterostructures studied here show large saturation andremanent polarization. Unlike homogeneous ferroelectricthin films, in compositionally-graded heterostructuresthe large strain gradients and variations in the chemicalcomposition can generate built-in potentials7,8,22,51,52

which can be quantified by the horizontal shift of theferroelectric hysteresis loopalong thevoltage (orfield) axis(i.e., the difference between the coercive field). Note thatthese built-in potentials are innate to the compositionally-graded materials (in its current strain state) and care wastaken to exclude additional effects that can give rise toshifts by using symmetric, perovskite-based, epitaxialSrRuO3 top and bottom electrodes.53

On the basis of common understanding of flexo-electric effects and built-in potentials,7,17,18,27,54 onewould empirically expect that the magnitude of thebuilt-in potential would be primarily governed by themagnitude of the strain gradient. Thus, for the thicknessseries of (20,80) heterostructures (Figure 4a), the magni-tude of the built-in potential should be inversely propor-tional to the thickness. The actual results, however, donot follow this trend, and instead, the built-in potential isfound to increase with film thickness until falling drama-tically in the case of the 150 nm thick heterostructures.Themeasured built-in potential was found to be 0.380(0.045 V (76( 9 kV/cm), 0.833( 0.038 V (111( 5 kV/cm),

Figure 3. Vertical phase piezoresponse force microscopy images of PbZr0.8Ti0.2O3 T PbZr0.2Ti0.8O3/SrRuO3/GdScO3 (110)heterostructures (sample name: (x,y)) (a) 50 nm (20,80), (b) 100 nm (20,80), (c) 150 nm (20,80), (d) 100 nm (20,45), and(e) 100 nm (40,60). A vertical amplitude piezoeresponse forcemicroscopy image is provided as an inset in each of the figures.

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2.00( 0.090 V (200( 9 kV/cm), and 0.4( 0.020 V (20(1 kV/cm) for the 50, 75, 100, and 150 nm thick (20,80)heterostructures, respectively.Only by returning to the differences in the crystal

and domain structure can this trend be explained.

Overall, as the thickness of the film increases themaximum average theoretical strain gradient andresidual strain decreases, and therefore, (under theassumption that the built-in potential is primarilygoverned by the strain gradient) the built-in potentialshould monotonically decrease with thickness. In turn,this suggests that additional contributions to the built-in potential must be present. To shed more light onthis concept, we can establish a frame of referencefor the “intrinsic” strain- and composition-gradient con-tribution to the built-in potential by first consideringthe 50 nm thick (20,80) heterostructures. These hetero-structures, which are coherently strained and mono-domain, possess a structuremost closelymatchedwiththe “ideal” compositionally- and strain-graded hetero-structure concept. Following the methods used inthe community,51 we can extract a coefficient of thesame form and units as the flexoelectric coefficient,which we here call the effective flexo-chemo-electric

coefficient, to acknowledge the inclusion of additionalcontributions, such as chemical-gradient effects, which arenot traditionally considered in the flexoelectric coefficient.Knowing that the strain gradient is 8.7 � 105 m�1 andthat the built in potential is 0.38 V, we calculate theeffective flexo-chemo-electric coefficient to be |μeff| =12 nC/m (see Supporting Information for details). Thisvalue lies directly in-between experimentally reportedflexoelectric coefficients for the PbZr1�xTixO3 system(500�2,000 nC/m,measured via bending of chemicallyhomogeneous samples)18,23,51 and first-principles cal-culations (which include only strain-gradient-basedflexoelectric effects; for PbTiO3 μ = 0.165 nC/m).26�28

This comparison brings up a number of interestingpoints. First, as is typical, our experimental measuresof these effects return valuesmuch larger than the first-principles predictions suggesting that additional con-tributions to these effects could be present. Second,our experimental values are considerably smaller thanmost experimental values, which might suggest thatthe chemical-gradient effect could be of the oppositesign to that of the classic strain-gradient effects.Using this effective flexo-chemo-electric coefficient,

we can thenmake a simple prediction of how the built-in potential should scale with thickness (dashed line,Figure 4c); since the maximum theoretical strain gra-dient is inversely proportional to the heterostructurethickness the built-in potential should fall of withincreasing thickness. What is clear, however, is thatthe built-in potentials measured for the 75 and 100 nmthick (20,80) heterostructures variants are greatly en-hanced compared to this expected trend. To explainthis unexpected observation requires consideration ofthe strain state and domain structure of the hetero-structures. Both the 75 and 100 nm thick (20,80)heterostructures exhibit a c/a/c/a domain structurewhere the size and density of the a domains increaseswith thickness, matching the observed trend in the

Figure 4. Room temperature polarization�electric fieldhysteresis loops of PbZryTi1�yO3 T PbZrxTi1�xO3/SrRuO3/GdScO3 heterostructures (sample name: (x,y)) measured at1 kHz of various (a) (20,80) heterostructure thicknesses and(b) various 100 nm thick compositional-gradient designs.(c) Plot of measured built-in potential as a function of filmthickness for all compositionally-graded heterostructures stu-died. Dashed line and small diamond markers represents anestimation of the built-in potentials based on the flexo-chemo-electric coefficient of the 50 nm (20,80) heterostructures.

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built-in potential. This implies that the formation offerroelastic domains could be responsible for the largerbuilt-in potential. We hypothesize that the presence offerroelastic a domains, and the corresponding rotationof the polarization direction at such domain bound-aries, gives rise to large, localized strain gradients16,31

and fields31,32 that contribute to the built-in potential.Since the largest built-in potential is observed in the100 nm thick (20,80) heterostructures despite thesignificant reduction in strain gradient, this suggeststhat the c/a/c/a domain structures are key in definingthe evolution of these effects. Finally, in the 150 nmthick heterostructures, which possess the most severestrain relaxation and domain structures indicative ofcomplete or near-complete relaxation at the surfaceof the film, the relaxation must be severe enough toreduce the overall magnitude of the strain gradient inthe film thereby reducing the overall built-in potential.A similar analysis of the built-in potentials for the

100 nm thick (20,45), (40,60), and (20,80) heterostruc-tures (Figure 4b), where the built-in potentials weremeasured to be 0.64 ( 0.03 V (64 ( 3 kV/cm), 1.5 (0.09 V (150( 9 kV/cm), and 2.0( 0.09 V (200( 9 kV/cm),respectively, can be completed. Recall that the theo-retical strain gradients for the (20,45) and (40,60) hetero-structures are approximately half of that of the (20,80)heterostructures and that both heterostructures exhibita monodomain structure. Beginning with the (40,60)heterostructures, the lattice parameters defining thestrain gradient increase rapidly, in a nonlinear fashion,upon transitioning through the MPB composition,55

we hypothesize that the presence of locally enhancedstrain gradients within the film associated with the MPBcompositions could greatly increase the magnitude ofthe macroscopic built-in potential, even in the absenceof domain structures. It should be noted, that hetero-structures encompassing the MPB could also exhibitenhanced built-in potentials because of a local variationin the magnitude of the flexoelectric coefficient, whichis typically larger near theMPB.27,56 Additionally, the factthat the built-in potential of the (40,60) heterostructuresare larger than that of the 50 nm thick (20,80) hetero-structures suggests that the chemical-potential-gradienteffects are likely smaller (because of the reduced com-positional range) and are still of the opposite sign of thestrain-gradient effects, pointing to a dependence similarto that for the strain-gradient effects on the compositionrange and thickness for the compositional-gradienteffects. On the other hand, in the (20,45) heterostruc-tures the reducedbuilt-in potential is like the result of thefact that the composition range probed exists entirelyin the tetragonal phase region of the PbZr1�xTixO3

phase diagram and that the lattice parameters increasesmoothly with increasing Zr content thereby excludingany locally enhanced strain gradients in the films. Ad-ditionally, the chemical-gradient effects in the (20,45)heterostructures should also be relatively smaller

in magnitude (compared to the 50 nm thick (20,80)heterostructures), but again we cannot fully decouplethe effects in a manner that allow us to quantify themagnitude of this chemical-gradient effect uniquely.All told, the ultimate manifestation of built-in potentialin the compositionally-graded heterostructures variesin a rather complex and, at times, unintuitive manner asa function of film thickness, lattice parameter variation,domain formation, strain relaxation, compositional endmembers, and much more. Overall, the built-in poten-tials are larger when locally enhanced strain gradientsexist such as occur upon transitioning through the MPBcomposition and at/near ferroelastic domain bound-aries. These observations suggest that the macroscopicmanifestation of built-in potential includes aspects offlexoelectric effects (i.e., polarization�strain gradientcoupling), chemical-gradient effects (i.e., polarization�chemical potential gradient coupling), and local inhomo-geneities that enhance strain (and/or chemical) gradientswhich occur in areas with rapid lattice parameter evolu-tion like near the MPB composition or near ferroelasticdomain boundaries.From a materials design perspective, however, we

care about the nature of and how to control the built-inpotential of these heterostructures because it can haveprofound effects on the nature of material properties.Prior studies of compositionally-graded PbZr1�xTixO3

heterostructures suggest that the presence of built-inpotentials can reduce the dielectric permittivity10,57 byacting to stiffen both intrinsic (i.e., with the bulk ofa domain) and extrinsic (i.e., from motion of domainwalls) responses to excitation under application ofsmall ac fields. Reducing the permittivity is key tooptimizing these materials for advanced nanoscaleapplications where the figure of merit for bothelectromechanical58�60 (k2 = e2/cεrε0, where e is thedirect-effect piezoelectric coefficient and c is the ma-terial stiffness, εr is the dielectric permittivity, and ε0 isthe permittivity of free space) and thermal59,61,62

(k2 = π2T/Cpεrε0, where π is the pyroelectric coefficient,T is the temperature of operation, and Cp is the heatcapacity) devices is defined by so-called coupling fac-tors. Routes to tune material stiffness, heat capacity, etc.are limited and thus the ability to tune these figures ofmerit is confined to routes that decouple the piezo-electric or pyroelectric coefficients from the permittivity.To quantify the combined influence of the crystal

and domain structure and built-in potential on thesusceptibility, the low-field dielectric permittivity wasmeasured as a function of frequency for all hetero-structures (for brevity, we show characteristic permit-tivity measurements at an ac excitation of 8 mV from1 to 100 kHz). Again, we begin by exploring thethickness series of (20,80) heterostructures (Figure 5a;dielectric loss is provided in the Supporting Informa-tion, Figure S6) where the dielectric permittivity wasfound to be 71.8, 68.5, 86.2, and 158.2 (at 10 kHz) for 50,

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75, 100, and 150 nm thick heterostructures, respectively.Beginningwith the 50 nm thick heterostructures (whicharemonodomain,withabuilt-inpotential of76(9kV/cm)the permittivity is suppressed to a value lower than thatpreviously reported for intrinsic permittivity (∼90) formonodomain, homogeneous PbZr0.2Ti0.8O3 thin films.63

This observation is readily understood since there areno extrinsic contributions (since there are no domainwalls) combinedwith the sizablebuilt-inpotential, whichserves to reduce the intrinsic susceptibility and thusthe overall response. As the heterostructure thicknessincreases, domain structures emerge that influence thepermittivity in competing ways. The presence of ferroe-lastic domains is known to give rise to extrinsic contri-butions to the dielectric permittivity, which typicallyenhance the dielectric permittivity,64�66 and this workhas shown that their formation also corresponds to anincreases the magnitude of the built-in potential, whichshould work to suppress both the intrinsic and extrinsiccontributions. Thus, in the 75 nm thick heterostructures(where there is a small density of domains and a largerbuilt-in field (111( 5 kV/cm), the combinationmanifestsas a similar dielectric permittivity to the 50 nm thickheterostructures (within the error of measurement). Bythe time the thickness reaches 100 nm, however, the

presence of a robust and denser domain structure andthe associated extrinsic contributions to the dielectricpermittivity overcomes the effects of the built-in field(200( 9 kV/cm), causing a slight increase in permittivity(although it is still smaller than that reported for mono-domain, homogeneous PbZr0.2Ti0.8O3 films). Finally, inthe 150 nm thick heterostructures, which have complex,mosaic-like domain structures, with the smallest built-inpotential of 20 ( 1 kV/cm, the largest permittivity isobserved; a result of the minimally suppressed intrinsicand extrinsic contributions to permittivity.Using a similar approach, we can also understand

the evolution of the permittivity in the 100 nm thick(20,45), (40,60), and (20,80) heterostructures (Figure 5b).In this set of heterostructures, the (20,45) variants havethe largest permittivity (∼107.5 at 10 kHz) and the(40,60) heterostructures have the lowest permittivity(∼64.4 at 10 kHz). Again, we can rationalize thesetrends through the combination of the crystal anddomain structure and built-in potential evolution.First, for the (20,45) heterostructures (with mono-domain structure and a built-in potential of 64 (3 kV/cm), the measured permittivity is close to theexpected permittivity for a monodomain, homo-geneous PbZr0.2Ti0.8O3 thin film,63 indicating thatthe dielectric response is dominated by the intrinsicresponse of the monodomain structure, and that thesmall built-in potential does not significantly influencethe dielectric response. For the (40,60) heterostruc-tures (with monodomain structure and sizable built-inpotential of 150( 9 kV/cm), the larger built-in potentialgreatly reduces the intrinsic permittivity, and sincethere are no domain walls, there is no extrinsic con-tribution resulting in the lowest observed dielectricresponse. We note that to the best of our knowledge,that these are the lowest permittivity values reportedfor any PbZr1�xTixO3 thin film system to date. Progres-sing to the (20,80) heterostructures, c/a/c/a domainstructures are formed generating an extrinsic re-sponse, which enhances the permittivity more thanthe increase in built-in potential can suppress it, caus-ing a slight increase in permittivity compared to the100 nm thick (40,60) heterostructures. Regardless, theobservation of the lowest reported room temperaturedielectric permittivity for the PbZr1�xTixO3 system,measured in the (40,60) heterostructures, which arecompositionally close to the MPB (where a maximumin dielectric permittivity should be expected) demon-strates the efficacy of compositional-gradients in gen-erating built-in potentials, which can provide routes tostrongly decouple the ferroic and dielectric responses.Altogether, through judicious exploration of a range

of nanoscale controlled, compositionally-graded het-erostructures, we have demonstrated that the ferro-electric and dielectric response is highly influenced bythe crystal and domain structure which can be ma-nipulated by the heterostructure design. Specifically,

Figure 5. Roomtemperaturedielectricpermittivity (measuredat Vac = 8 mV, error <7%) as a function of frequency forPbZryTi1�yO3 T PbZrxTi1�xO3/SrRuO3/GdScO3 compositionally-graded heterostructures (sample name: (x,y)) for various (a)(20,80) heterostructure thicknesses and (b) various 100 nmthick compositional-gradient designs.

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we show that the magnitude of the built-in potentialis only minimally influenced by the magnitude of theaverage strain gradient and instead is determined acombination of flexoelectric effects (i.e., polarization�strain gradient coupling), chemical-gradient effects(i.e., polarization�chemical potential gradient coupling),and local inhomogeneities that enhance strain (and/orchemical) gradients such as areas with rapid latticeparameter evolution like that near theMPB compositionor near ferroelastic domain boundaries. This work high-lights the importance of local nanoscale strain gradientsin generating large macroscopic built-in potentials,yielding new perspectives on how to design ferroelec-tric thin films to maximize built-in potentials whilehaving minimal effect on the ferroic responses. In turn,these results provide a facile route to independentlytune susceptibilities in ferroelectric thin films essentialfor optimizing materials figure of merit for a range ofnanoscale applications.

CONCLUSIONS

In summary, we have explored how deterministiccontrol of compositionally-graded heterostructureform (in terms of the nature of the compositionalgradient and heterostructure thickness) can be used

to tune the crystal and domain structure and what theinfluence of these changes are for the evolution ofbuilt-in potentials, ferroelectric, anddielectric responsein PbZr1�xTixO3 thin films. The magnitude of the built-in potential is found not to scale directly with themagnitudeof the strain gradient (aswouldbeexpected),but instead, large built-in potentials are observed in thecompositionally-graded heterostructures, which containlocally enhanced strain gradients that occur when tra-versing chemistries associated with structural phaseboundaries where there are abrupt changes in materiallattice parameter and at/near ferroelastic domainboundaries. These observations suggest that the built-in potential observed in these materials is likely amanifestation of a combination of flexoelectric effects(i.e., polarization�strain gradient coupling), chemical-gradient effects (i.e., polarization�chemical potentialgradient coupling), and local inhomogeneities that en-hance strain (and/or chemical) gradients. Regardlessof origin, large built-in potentials act to suppress thedielectric permittivity while having minimal impact onthe magnitude of the polarization, providing a facileroute to optimize these materials for a range of nano-applications from vibrational energy harvesting to ther-mal energy conversion and beyond.

METHODS

Film Growth. Compositionally-graded heterostructures ofPbZr1�xTixO3 (PZT)/30 nm SrRuO3/GdScO3 (110) were grownusing pulsed-laser deposition from Pb1.1Zr0.2Ti0.8O3 andPb1.1Zr0.8Ti0.2O3 targets.7 The bottom electrode SrRuO3 filmswere grown at 630 �C in an oxygen pressure of 100 mTorr ata laser fluence 1.8 J/cm2 and a frequency of 13 Hz. Thecompositionally-graded PZT layers were grown at 600 �C inan oxygen pressure of 200 mTorr, during the growth the laserfluence was maintained at 1.9 J/cm2, pulsed at a frequency of3 Hz. The composition of the compositionally-graded layerswas controlled by continuously varying the composition fromPbZrxTi1�xO3 to PbZryTi1�yO3 using a programmable targetrotator (Neocera, LLC) that was synced with the excimer laser.For all the samples, films were cooled in an oxygen pressureof 700 Torr. Symmetric capacitor structures were fabricated bysubsequent deposition of 80 nm SrRuO3 top electrodes definedusing a MgO hard-mask process.67

Crystal Structure and Ferroelectric Domain Structure Analysis. Thestructure of these heterostructures was studied using X-ray dif-fraction reciprocal space mapping (RSM) about the 103- and332-diffraction conditions for the film and substrate, respec-tively. We utilize the Four-circle High Resolution X-ray Diffract-ometer (PANALYTICAL X'PERT PRO). Detail ferroelectric domainanalyses of the filmswere carried out using Piezoresponse ForceMicroscopy (Cypher, Asylum research).

Dielectric and Ferroelectric Properties. The dielectric permittivitywas extracted from the measured capacitance (C) using C =((ε0εrA)/d) where A is the area of the capacitor and d is thethickness of the film. Prior tomeasurement, the films were poledwith a negative bias for 0.1 ms and films were measured atremanence. The dielectric permittivity as a function of frequencywas measured with an ac excitation voltage of 8 mV (rms).Rayliegh studies confirmed that the ac excitation was smallenough to preclude irreversible domain wall motion. Ferroelec-tric hysteresis loops weremeasured using a Radiant MultiferroicsTester as a function of frequency from 0.1�20 kHz.

Conflict of Interest: The authors declare no competingfinancial interest.

Acknowledgment. J.C.A. and L.W.M. acknowledge supportfrom the National Science Foundation under grant numberDMR-1451219. A.R.D. and S.P. acknowledge the support of theArmy Research Office under grant number W911NF-14-1-0104.R.V.K.M. acknowledges support from the National ScienceFoundation under grant ENG-1434147.

Supporting Information Available: Additional X-ray diffrac-tion studies, determination of residual strain in compositionally-graded heterostructures, additionally reciprocal spacemappingstudies, additional piezoresponse force microscopy studies,additional ferroelectric hysteresis loops and dielectric lossmeasurements. The Supporting Information is available freeof charge on the ACS Publications website at DOI: 10.1021/acsnano.5b02289.

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